Interactions of the b-cyclodextrin (b-CD) ligand with Na ? , Cu ? , Mg 2? , Zn 2? , and Al 3? cations were investigated using density functional theory modeling. The objective of this study was to give insight into the mechanism of cation complexation. Two groups of conformers were found. The first group preserved the initial orientation of glucopyranose residues inside the b-CD ligand. The mutual orientation of glucopyranose residues was strongly affected by the cation in the second group of conformers. The system interaction energy was decomposed into electrostatic (ES), Pauli and orbital contributions using the Ziegler-Rauk energy partitioning scheme. The total electrostatic energy, i.e., the sum of ES energy and polarization energy, is the dominating term in the interaction energy. In vacuum, the complexes formed with Al 3? were found to be more stable than with di-and monocations. The vacuum stability sequence was changed in aqueous solution.

Charge sensitivity analysis (CSA) was extended to AMBER force-field resolution. The effective electronegativity and hardness data were found using evolutionary algorithms. Four model hardness matrices based on the classical electrostatic, Mataga-Nishimoto, Ohno, and Louwen-Vogt interpolation formulae were considered. Mulliken population analysis and electrostatically derived charges (CHELPG) were taken into account. It was demonstrated that the Ohno interpolation formula gives the best fit to Mulliken charges. For all molecules from the training set and all model hardness matrices, Mulliken charges were reproduced more accurately than CHELPG charges, indicating their good transferability from system to system. The effective electronegativities and hardnesses obtained were further verified by applying CSA to molecules from a validation set that was different from the training set. The correlation between CSA and Mulliken charges was of the same quality as that obtained for the training set.

Charge sensitivity analysis was originally introduced in the trivial-atom resolution. Here, we extend this resolution into force-field atoms. The AMBERff99 force-field resolution was employed. The effective electronegativities and hardnesses were derived for five different population analyses (Mulliken, Hirschfeld, AIM, NPA and Voronoi charges) by applying evolutionary algorithms.

A simple way to improve the accuracy of the fragmentation methods is proposed. The formalism was applied to the elongation (ELG) method at restricted open-shell Hartree-Fock (ROHF) level of theory. The α-helix conformer of polyglycine was taken as a model system. The modified ELG method includes a simplified electrostatic field resulting from point-charge distribution of the system’s environment. In this way the long-distance polarization is approximately taken into account. The field attenuates during the ELG process to eventually disappear when the final structure is reached. The point-charge distributions for each ELG step are obtained from charge sensitivity analysis (CSA) in force-field atoms resolution. The presence of the intermediate field improves the accuracy of ELG calculations. The errors in total energy and its kinetic and potential contributions are reduced by at least one-order of magnitude. In addition the SCF convergence of ROHF scheme is improved.

Charge sensitivity analysis (CSA) in force-field atoms resolution was applied to describe the mutual polarization of reactants as well as charge-transfer (CT) effects. An inclusion complex of β-cyclodextrin with salicylic acid was used as a model system. Three CSA models were taken into account and verified on a Born–Oppenheimer molecular dynamics (BOMD) trajectory. The models differed in terms of the equilibrium conditions imposed on the system. It was demonstrated that mutual polarization is an important source of stabilization, in contrast to the results obtained from static charge calculations. The energy lowering induced by CT was small and comparable to the CT stabilization that occurs in hydrogen-bonded systems. All models correctly described the main topological features of the BOMD energy surface. CSA in force-field atoms resolution qualitatively reproduced the charge reorganization accompanying hydrogen-bond formation. It was shown that CSA parameters are very sensitive to the bond formation process, which suggests that they could be applied in reactive force fields as detectors of newly formed chemical bonds.FigureFukui function detector of bond formation during molecular dynamics simulations of inclusion complex of b-cyclodextrin with salicylic acid.Electronic supplementary materialThe online version of this article (doi:10.1007/s00894-013-1757-4) contains supplementary material, which is available to authorized users.